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% Black-Scholes forward greeks
% only output theta and dollar-greeks
% Liuren Wu, liurenwu@gmail.com
%%%%%%%%%%%%%
function [Theta, dVega, dGamma, dVanna, dVolga] = FunForwardVGVVGreeks(F, d1, I, T)
VT=I.*sqrt(T);	VT2=VT.^2; F2=F.^2;I2=I.^2;
d2=d1-VT;
zp=-d2.*VT;
zm=-d1.*VT;

Gamma = normpdf(d1)./(F.*VT);
dGamma=Gamma.*F2; %dollar gamma
Theta=-.5*I2.*dGamma; %theta

dVega=VT2.*dGamma; %dollar vega
dVanna=zp.*dGamma;  %dollar vanna
dVolga=zp.*zm.*dGamma; %dollar volga

